analysis of deformation of a liquid packaging made … of deformation of a liquid packaging made...

Analysis of Deformation of a Liquid Packaging Made with Board

of the LPB Type.

K. B. Matos*1, I. Neitzel2 1FATEB, 2 FATEB * Author for correspondence: 517 Ozório de Almeida Taques Avenue, apt A7-22, 84261680, Telêmaco Borba,

PR, Brazil, 84261680 < [email protected]>

Abstract: The liquid food products packaging are

now predominantly made with LPB type board

(Liquid Packaging Board), derived from the

pulping process, polyethylene and aluminum. In

the storage process such packages deform

plastically and elastic. Then, it aimed to analyze

the deformation profile of a simplified packaging,

made only with board without rolling of

aluminum and polyethylene, and parametrically

vary the elastic constants of the material. The

results indication that the strain profile is function

of the density of the liquid packaged in the

packaging, the elastic constant of the board,

mainly Poisson's ratio, and it was possible to

establish the main equations governing the

deformation profile.

Keywords: Deformation, Liquid Packaging,

LPB, Paper.

1. Introduction

Currently, general packaging have wide scope

in their use. Besides of the basics functions that

include the physical and chemical protection,

shipping and handling, were incorporated to

packaging the information functions and visual

communication. They can be produced from

different materials such as wood, paper, board,

metal, aluminum, glass, polymers and textile

materials (NESPOLO, 2015).

The carton packaging are defined to as a six-

layer composite comprising paper, low density

polyethylene and aluminum, these containers

known as Long Life represented by Figure 1.

A descriptive analysis reveals that aluminum,

polyethylene and board sequentially represent

5%, 20% and 75% of the total pack weight

(PERUZZO, 2005).

Figure 1. Constitution of carton packaging

(NESPOLO, 2015).

The plastic in this case made from

polyethylene polymers, provides enhanced

resistance to water flow. The use of aluminum

foil, can give the container different degrees of

stiffness, depending on the thickness, shape and

alloy. By itself, the aluminum foil does not

provide high barrier against the flow of oxygen

due to its high porosity, but when coated with

polyethylene, its efficiency is improved because

in this case the holes are covered. The use of

paper, consisting of virgin fibers (primary)

coming from the Kraft process and CTMP

(chemithermomechanical pulp), provides

packaging characteristics of strength and opacity,

this component will be further detailed in the

following sections.

1.2 Paper and Board

On the day, paper and board are words used as

synonyms for each other. Are products obtained

from the pulping process, a process which is the

individualization of wood cells, called fibers.

Such processes can be classified as mechanical,

chemical or hybrid that mixes the use of chemical

and mechanical process steps. The following

Table 1 to statement of pulping process on the

yield of the obtained pulp (single fiber):

Excerpt from the Proceedings of the 2016 COMSOL Conference in Boston

Table 1- Classification of pulping processes based on

pulp yield (IPT, 1988)

Pulping Process Yield of wood

(%)

Mechanic 95 - 98

Chemical Thermo

Mechanical Pulping

85 - 95

Semi Chemical 65 - 85

High Performance Chemical 50 - 65

Chemical 40 - 50

Chemical to Soluble Pulp 30 - 40

The basic properties of any type of paper and

paperboard include moisture content, weight,

thickness, density and bulk; properties that

describe the product (LEVLIN, 1999).

The moisture content of paper it described by

ISO 287, is expressed as a percentage of the

weight of the wet sample.

The weight of paper, called a weight,

representing the quantity of mass in grams per

square meter (g/m2), as described by ISO 536.

The thickness measurement described by ISO

534, is given by a unit of two parallel plates which

apply the paper a 100 kPa pressure, thereby

obtaining normal expression of weight in microns

(µm); this value may be representative of a single

a sheet or the sheet set.

The apparent density is the mass per unit

volume of paper, calculated as the ratio of the

weight and thickness of the material, and is

usually expressed in kg/m3 or g/cm3. From the

apparent density is defined as the bulk, through its

inverse:

𝐵𝑢𝑙𝑘 =1

𝑑𝑒𝑛𝑠𝑖𝑡𝑦= [

𝑐𝑚3

𝑔] 𝑒𝑞(1)

According to the process of formation, the

paper is different board. The paper is formed from

the drainage of a fibrous suspension of cellulose

while the board is usually composed of several

sheets of cellulose fibers bound by starch or

adhesive. Also points to the fact that the term

board is used for heavy paper (XIA, 2002).

To check their physical and structural

properties, the paper has its oriented analysis in

three orthogonal directions: Machine Direction

(MD), Cross Direction (CD), and the Z Direction

(ZD). The MD direction is the longitudinal

direction of the paper corresponding to the

direction of movement of the continuous sheet on

the paper machine. The CD direction

corresponding to the direction perpendicular to

the movement of the web in the paper machine.

Both CD and MD directions, are in the plain

paper. The ZD orientation refers to the direction

out of the paper plane or through their thickness

(Andrioni, 2006).

For better representation, the following the

Figure 2 that represents a formed paper roll and

the Figures 3 and 4, that structurally represent the

paper and board sequentially.

Figure 2. Orientation on a paper roll (NESPOLO,

2015).

Figure 3. Design macro and micro structural of the

paper (XIA, 2002).

Figura 4. Design macro and micro structural of the

paper roll (XIA, 2002).

1.3 Paper and Board Elastic Constants

The elastic constants give the paper the stress-

strain relation in the elastic region. The main ones

are the Modulus of Elasticity (E), Shear Modulus

(G) , and Poisson's ratio (𝜈). For the analysis of

elastic symmetry of materials, there is four

classifications: homogeneous materials, isotropic

materials, orthotropic and anisotropic ( NASH,

2014):


Homogeneous material, when the elastic

property (E, G, ν) are the same in any point of

the examined body;

Isotropic materials having the same elastic

properties (E, G, ν) in all directions of the

body;

The orthotropic material have three mutually

perpendicular planes, and elastic symmetry

between them;

The anisotropic materials do not have any kind

of elastic symmetry.

The behavior of materials during a charging

process reveals itself in two ways: elastic and

plastic. A material has elastic behavior after the

process of loading and load removal, there are

deformations in the body. If the specific strain (ε)

does not return to zero, conceptualizes up their

behavior as plastic or permanent plastic

deformation. For better representation of such

deformations, the following figures 5 and 6, these

images illustrating the elastic and plastic

deformations of a generic packaging liquid food

products.

Figure 5- Representation of elastic deformation (front

and side)

Figure 6- Representation of plastic deformation (front

and side)

2. Methodologies

This article is a simplified study, which aims

to evaluate the deformation of a package made

only with board LPB type, without the presence

of polyethylene and aluminum. It is also proposed

the equation that governs the process as well as

the analysis of the properties of the board and the

liquid bottled in the packaging deformation

profile. The effect of an external load

corresponding to a second container, as well as the

effect of temperature were not considered.

The material was considered as orthotropic,

and the MD orientation of the board in the

direction of the height of the packaging and the

board CD orientation in the circumferential

direction to it. Through the tool "parametric

sweep", the elastic constants of the material were

parametrically varied in a specified range around

the I note the representative value on the

theoretical reference as well represented by Table

2:

Table 2 - variation range of the board properties

Variable Units Minimum Maximum

Liquid Density 800 1200

Board Density 600 1500

Young Modulus (MD) 5000 8000

Young Young Modulus (CD) 3000 4600

Poisson (MD) - 0,2 0,45

Poisson (CD) - -2,5 0,4

Shear Modulus (MD) 1000 3500

Shear Modulus (CD) 8,8 15000

𝑘𝑔 𝑚3

𝑘𝑔 𝑚3


Through Solid Mechanics Module, was

inserted the effect that the presence of liquid

causes inside the package using pressing tools

without the physical presence of the liquid.

After making the simulation of the

deformation process, was evaluated the variation

of lateral and upper volumes for equalization and

better discussion of the results according to figure

7.

Figure 7- Analysis of the volume variation

For comparison of results was measured at a

real deforming packaging through the use of

hydraulic jack, and caliper slider, this scheme

represented in Figure 8.

Figure 8- Project for measurements

3. Equations e Results

The structural model initially proposed, as

presented deformation Figure 9. The values are

shown three-dimensionally in millimeters on a

scale of 2,42, i.e., 2.42 times larger than the actual

deforming to better interpret the results visually.

This simulation was made in order to verify the

behavior if the package remained open in the

environment without any restrictions.

Figure 9- deformation profile analysis in millimeters

with volumetric variation

At this early stage of the simulation, the

parabolic profile deformation in the larger

surfaces of the packaging, this profile that

resembles this deformation in open containers

was obtained.

It was observed that the smaller faces moving

towards the inner region of the package, while the

larger faces move to the outer region. Therefore it

equated to volume constraint followed by

Equation 2 and 3 so as to represent the initially

closed package:

∆𝑉 = ∆𝑉𝑒𝑥𝑝𝑎𝑛𝑠𝑖𝑜𝑛 + ∆𝑉𝑐𝑜𝑚𝑝𝑟𝑒𝑠𝑠𝑖𝑜𝑛 = 0 𝑒𝑞(2)

∆𝑉𝑐𝑜𝑚𝑝𝑟𝑒𝑠𝑠𝑖𝑜𝑛 = ∆𝑉𝑒𝑥𝑝𝑎𝑛𝑠𝑖𝑜𝑛 𝑒𝑞(3)

where ∆𝑉𝑐𝑜𝑚𝑝𝑟𝑒𝑠𝑠𝑖𝑜𝑛 is the volumetric variation

generated by the displacement of the smaller sides, and

∆𝑉𝑒𝑥𝑝𝑎𝑛𝑠𝑖𝑜𝑛 is the volume variation generated by the

displacement of the larger sides.


To this proposed equation, we used the tool

"Global Constraint", made this way the

deformation profile shown in Figure 10:

Figure 10- deformation profile analysis in millimeters

with volume restriction.

For a two-dimensional graphical analysis with

the aid of the "Cut line 3D" tool was analyzed

deformation of the largest side according to the

graph 1, where the abscissa represents the height

of the package in centimeters, and the ordinate the

value of the deformation in mm . The obtained

deforming was named Profile Profile "S".

Graphic 1- Profile “S” of deforming.

Later, comparison of the deformation

obtained through COMSOL Multhiphysics

software with the deformation of a real packaging

was performed, thereby generating the graph 2

annexed in this article.

There are variations in the deformation

obtained through software and experimental

measurements. Factors such as the process of

measuring the real packaging, presence of folds,

absence of polyethylene and aluminum rolling

can justify such deviation. To enhance the

discussion between the results obtained from the

COMSOL software and experimental, they were

varied the elastic constants of the board according

to Table 2.

The analysis density of board showed no

influence on the packaging deforming profile, as

represented by Graph 3, where both graphics

overlap.

Graph 3- Deformation depending on the density of

board.

Later it was varied other elastic constants of the

board, both in the direction MD and in CD

direction. Both results demonstrate that generated

the largest amplitude variation is a function of

changes in direction contained in the CD, as

shown by the graphs 4 and 5, in which was varied

the modulus of elasticity of the material. This

effect can be explained by the concept of pressure

vessels, where the highest pressure occurs in the

circumferential direction of the package.


Graph 4- Deformation due to the variation of the MD

Elasticity Module (5GPa <E <8GPa).

Gráfico 5- Deformation as a function of variation of

CD elasticity module (3 GPa <E <6 GPa).

Finally, to check the influence of the change

in the density of the liquid the bottled in the

package on the deformation, the liquid density

was varied in a range comprising 800 kg.m-3 to

1200 kg.m-3. Results obtained by the following

Graph 6 which shows significant influence on the

deformation profile on the basis of the variation

of the density of the liquid bottled in the

packaging.

Graph 6- Deformation due to the variation of the

density of the packaged fluid (800𝑘𝑔

𝑚3 to 1200 𝑘𝑔

𝑚3) .

4. Conclusion

It was possible to evaluate the profile of the

deformation of a packaging made of board type of

LPB, the influence of variations of the elastic

constants of the board and the density of the liquid

the bottled in the package on the deformation.

Equating proposed for the closed container, with

restriction internal volume, was the potential

equation that governed the deformation profile.

The results indicate the study considering the

composite board with polyethylene and

aluminum, as well as the optimization of physical

measurement method of the actual package.

5. References

Andrioni, José Luís Lino. Fabricação de Papel-

Formação de Folha. Curitiba, 2006;

IPT- Instituto de Pesquisas Tecnológicas.

Celulose e Papel, Tecnologia de Fabricação de

Pastas - Vol I. Segunda Edição. São Paulo: IPT.,

1988;

Levlin, J.E.; Söderhjelm, L.. Pulp and Paper

Testing. Editora Finnish Paper Engineers’

Association. Book 17, 2ª edição,1999;


Nash, William A. Nash, Merle C. Potter.

Resistência dos Materiais. 5 ed. E. Bookman. Rio

Grande do Sul: Porto Alegre. 2014;

Nespolo, Cássia Regina, Fernanda Arboite de

Oliveira, Flávia Santos Twardowski Pintoe

Florencia Cladera Olivera. Práticas em

Tecnologia de Alimentos. Artmed Editora, 2015;

Peruzzo, Cicília Krohling. Produção Visual e

Gráfica. Editora Summus Editorial, 2005;

Xia, Qingxi S., Mary C. Boyce, David M. Parks,

A constitutive model for the anisotropic elastic–

plastic deformation of paper and paperboard,

International Journal of Solids and Structures, 39,

4053–4071, 2002.


Annex 01.

Graph 2- Comparison of Deformation Measurement and Simulated

Orange points represent the deformation obtained by the software, and blue points deformation measured experimentally.

-4,00

-3,50

-3,00

-2,50

-2,00

-1,50

-1,00

-0,50

0,00

0,50

1,00

0 2 4 6 8 10 12 14 16 18

De

form

atio

n (

mm

)

Height

Actual Measurement

COMSOL


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